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arXiv:1003.2830

Two-Time Quantum Mechanics

Natalia N. Gorobey, Alexander S. Lukyanenko, Inna Lukyanenko

Published Mar 14, 2010• 0 citations
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Abstract

A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
DOI
10.48550/arxiv.1003.2830

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Within the framework of stochastic calculus of variations for time-symmetric semimartingales X(t,ω), we consider two different stochastic versions of Maupertuis’ least action principle, in Lagrangian and Hamiltonian terms. The general results are applied to classical statistical mechanics, where they coincide with those of classical calculus of variations, and to Nelson’s stochastic mechanics, an approach to quantum mechanics where a time-symmetric semimartingale represents the position of a particle and the dynamics is expressed by a stochastic version of Hamilton’s principle of least action. Some historic examples of old quantum theory are discussed.